\[ \int \frac {\sqrt {1-2 x} (2+3 x)^5}{(3+5 x)^2} \, dx \]
Optimal antiderivative \[ -\frac {328 \arctanh \left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}}{859375}-\frac {172 \left (2+3 x \right )^{2} \sqrt {1-2 x}}{3125}+\frac {64 \left (2+3 x \right )^{3} \sqrt {1-2 x}}{2625}+\frac {11 \left (2+3 x \right )^{4} \sqrt {1-2 x}}{75}-\frac {\left (2+3 x \right )^{5} \sqrt {1-2 x}}{5 \left (3+5 x \right )}-\frac {4 \left (10998+3625 x \right ) \sqrt {1-2 x}}{15625} \]
command
integrate((2+3*x)**5*(1-2*x)**(1/2)/(3+5*x)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {27 \left (1 - 2 x\right )^{\frac {9}{2}}}{200} - \frac {8829 \left (1 - 2 x\right )^{\frac {7}{2}}}{7000} + \frac {107109 \left (1 - 2 x\right )^{\frac {5}{2}}}{25000} - \frac {144681 \left (1 - 2 x\right )^{\frac {3}{2}}}{25000} + \frac {6 \sqrt {1 - 2 x}}{3125} - \frac {44 \left (\begin {cases} \frac {\sqrt {55} \left (- \frac {\log {\left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} - 1 \right )}}{4} + \frac {\log {\left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} + 1 \right )}}{4} - \frac {1}{4 \left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} + 1\right )} - \frac {1}{4 \left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} - 1\right )}\right )}{605} & \text {for}\: \sqrt {1 - 2 x} > - \frac {\sqrt {55}}{5} \wedge \sqrt {1 - 2 x} < \frac {\sqrt {55}}{5} \end {cases}\right )}{15625} + \frac {326 \left (\begin {cases} - \frac {\sqrt {55} \operatorname {acoth}{\left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} \right )}}{55} & \text {for}\: x < - \frac {3}{5} \\- \frac {\sqrt {55} \operatorname {atanh}{\left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} \right )}}{55} & \text {for}\: x > - \frac {3}{5} \end {cases}\right )}{15625} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________